There may be lots of problems with emergencies all over the world, but dialing the actual number isn’t one of them.

well, there's a couple benefits i can see to a quick-dial: in an emergency situation time is of the essence and you want as little hassle as possible in reaching emergency services. maybe for some reason you can't dial well, or at all--maybe you're panicking and a shortcut button gives you a less entropic way of calling emergency services.